Fagnant et al. (2020): each line is a gauge from the same \(5^\circ \times 3^\circ\) region
Sample many realizations of weather to overcome sampling variability
Physically constrained; better extrapolate to future climates
Drizzle bias and dynamical limitations motivate downscaling / bias correction sampling variability is back in the picture!
Generic nonstationary model for annual maximum precipitation: \[ y(\mathbf{s}, t) \sim \text{GEV} \left( \mu(\mathbf{s}, t), \sigma(\mathbf{s}, t), \xi(\mathbf{s}, t) \right) \]
Process-informed models condition parameters on climate indices \(\mathbf{X}(t)\) (Cheng & AghaKouchak, 2014; Schlef et al., 2023) \[ \theta(\mathbf{s}, t) = \alpha + \underbrace{\sum_{j=1}^J \beta(\mathbf{s}) \mathbf{X}(t)}_{\text{nonstationarity model}\atop\text{more parameters}} \]
Serinaldi & Kilsby (2015): more parameters, same data more uncertainty
We use long-record gauges AND newer mesonets
Our Bayesian space-time model:
Represents medium-term changes to extreme precipitation probabilities
Reduces estimation uncertainty
Demonstrates well-calibrated inferences
Explicitly spatial (free interpolation)
Overcomes sampling variability
@jdossgollin